J. Phys. Chem. A 2006, 110, 8467-8476
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Two-Channel Dissociation of Chemically and Thermally Activated n-Butylbenzene Cations (C10H14+)† Abel I. Fernandez,‡,§ A. A. Viggiano,*,‡ and J. Troe| Air Force Research Laboratory, Space Vehicles Directorate, 29 Randolph Rd., Hanscom AFB, Massachusetts 01731-3010, and Institute for Physical Chemistry, UniVersity of Goettingen, Tammannstrasse 6, D-37077 Goettingen, Germany ReceiVed: NoVember 25, 2005; In Final Form: January 20, 2006
The charge-transfer reaction O2+ + n-butylbenzene (C10H14) f O2 + C10H14+* was studied in a turbulent ion flow tube at temperatures between 423 and 548 K and pressures between 15 and 250 Torr in the buffer gases He and N2. Under chemical activation conditions stabilization vs dissociation ratios S/D of vibrationally highly excited C10H14+* as well as branching ratios of the fragments C7H7+ (m/z ) 91) vs C7H8+ (m/z ) 92) of the dissociation of C10H14+* were measured. Under thermal activation conditions, the rate constant of the dominating dissociation channel 92 was measured at 498 and 523 K. Employing information on the specific rate constants k(E) of the two channels 91 and 92 and on collisional energy transfer rates from the literature, the measured S/D curves and branching ratios 91/92 could be modeled well. It is demonstrated that the charge transfer occurs approximately equally through resonant transfer and complex-forming transfer. The thermal dissociation experiments provide a high precision value of the energy barrier for the channel 92, being 1.14 ((0.02) eV.
1. Introduction The dissociation of n-butylbenzene cations (C10H14+) serves as a prototype for ion dissociations which proceed with competing channels1 and for which the specific rate constants ki(E) of the channels i could be established by absolute2,3 and relative2-15 rate measurements. At low energies, the two channels
C10H14+ f C7H7+ + C3H7 (m/z ) 91)
(1.1)
f C7H8+ + C3H6 (m/z ) 92)
(1.2)
dominate the reaction. Process 1.2 involves a McLafferty rearrangement with a reverse barrier,2 and process 1.1 forms benzylium ions by a simple bond fission without a reverse barrier. Process 1.1 may also produce tropylium ions in either a direct process with a reverse barrier or in a secondary process by isomerization of vibrationally highly excited benzylium ions formed in reaction 1.1. The latter was investigated in a study of the dissociation of ethylbenzene cations.16 The tropylium channel was found to be more important in smaller alkylbenzenes cation dissociations than in n-butylbenzene cation dissociation.16,23 The specific rate constants k92(E) of reaction 1.2 have been determined in absolute rate measurements by the photoelectron-photoion coincidence (PEPICO) technique in the milli- to microsecond time range2 and by photodissociation mass analyzed ion kinetic energy spectrometry (PD-MIKES) in the nanosecond time range.3 In addition, the branching ratio of the specific rate constants k91(E)/k92(E) (also denoted by 91/92) was measured by a variety of techniques2-15 and has served as a “molecular thermometer”2,12 allowing one to establish the †
Part of the “Chava Lifshitz Memorial Issue”. * Corresponding author. E-mail:
[email protected]. ‡ Air Force Research Laboratory. | Institute for Physical Chemistry, University of Goettingen. § National Academy of Sciences Postdoctoral Fellow.
internal energy E of C10H14+. Combining the absolutely measured k92(E) with the branching ratio k91(E)/k92(E) directly leads to the specific rate constant k91(E) of reaction 1.1. Both k91(E) and k92(E) have been modeled by standard rigid activated complex Rice-Ramsperger-Kassel-Marcus (RRKM) theory, which provided estimates of the kinetic shifts of single2,3,15 and competing channels15 of the reaction, which led to values of the threshold energies E0(91) and E0(92) of reactions 1.1 and 1.2, respectively. Threshold collision-induced dissociation (TCID) measurements were made on the reaction system15 as well, to determine the threshold energies of reactions 1.1 and 1.2. In ref 17, RRKM theory was superseded by statistical adiabatic channel model/classical trajectory (SACM/CT) calculations for the bond fission (1.1) where a fixed rigid activated complex loses its significance. The SACM/CT calculations allowed for a new determination of kinetic shifts and hence of the threshold energy E0(91) of reaction 1.1.17 The availability of specific rate constants k91(E) and k92(E) over wide energy ranges also allows one to study reactions 1.1 and 1.2 under more general conditions and to test a variety of methods for the analysis of rate parameters under less energyspecific conditions than applied in refs 2 and 3. This is the issue of the present work, in which chemically and thermally activated n-butylbenzene cations were produced and reacted to form the competing channels 1.1 and 1.2. In chemical activation experiments, vibrationally highly excited butylbenzene cations, C10H14+*, were formed by the charge exchange process
O2+ + C10H14 f O2 + C10H14+*
(1.3)
The use of our turbulent ion flow tube (TIFT) technique16,18-23 allowed us to employ sufficiently high pressures of a buffer gas (in the 15-300 Torr range) such that C10H14+* could be stabilized (S) in competition with dissociation (D) via channels 1.1 and 1.2. Measurements of the ratio S/D provide information on the stabilization rate if one can rely on the measurements of
10.1021/jp056846c CCC: $33.50 © 2006 American Chemical Society Published on Web 02/28/2006
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the dissociation rates described above. In particular, if the total rate coefficient for energy transfer between C10H14+* and the buffer gas M can be identified with the collision frequency Z, one may determine the average energy 〈∆E〉 transferred per collision. We have described experiments of this type for highly vibrationally excited ethylbenzene and n-propylbenzene cations in refs 22 and 23, respectively. Since only a small amount of information on 〈∆E〉 is available for molecular ions (from relative rate measurements such as described in refs 24-27), it appears worthwhile to perform S/D measurements on nbutylbenzene cations as well. It was suggested in refs 22 and 23 that charge exchange (1.3) proceeds by three mechanisms. A resonant process produces C10H14+* with an energy equal to the ionization potential difference between C10H14 and O2 plus the vibrational energy of C10H14. The second process involves a bound (O2-C10H14)+ intermediate complex which statistically partitions vibrational energy between O2 and C10H14+ upon dissociation such that C10H14+* contains less vibrational energy (and in a different distribution) than in the resonant process. Finally, electronically excited O2(1∆g) or O2(1Σg+) may be produced, such that C10H14+* contains even less vibrational energy. The present study of the n-butylbenzene cation system tests the hypothesis of several charge-transfer pathways. At sufficiently high pressures, thermally activated C10H14+ ions can be generated23,28,29 after collisional stabilization of chemically activated C10H14+* from reaction 1.3. If the temperatures are high enough, collisional stabilization and thermalization of C10H14+* is followed by thermal dissociation on a much longer time scale. Our earlier studies of ethylbenzene+ and n-propylbenzene+ pyrolysis have indicated that these reactions were in the high-pressure range of unimolecular dissociation.28 One may safely assume analogous behavior for the dissociation of n-butylbenzene cations under the same highpressure conditions. Our measurements of the thermal dissociation rates of n-butylbenzene cations are therefore complementary to the studies of dissociations of the energy-selected ions. In particular, literature values of the threshold energy E0(92) of reaction 1.2 vary substantially. These can be tested by analyzing our measured absolute value of the thermal dissociation rate constant since it very sensitively depends on E0(92). A further point of interest is to measure the branching ratio 91/92 in both chemical and thermal activation experiments and analyze it in terms of the ratios k91(E)/k92(E) from the detailed energy-specific measurements mentioned above. Like in earlier work, this ratio can serve as a molecular thermometer. In the present case, it allows us to deduce the relative importance of the different charge-transfer mechanisms for reaction 1.3 described above. Finally, the formation of a minor fragment at m/z ) 105, possibly arising from a process15
C10H14+ f C8H9+ + C2H5
(1.4)
was studied under chemical activation conditions. There is a practical nature to these studies. They contribute to a better understanding of the reactions of aromatic fuels with air plasma ions such as O2+ and NO+ and their subsequent reactions.16,18,22,23,30,31 These processes play a role in advanced hydrocarbon-fueled air breathing propulsion systems29,32 wherein combustion is required to occur on short time scales. It has been found that ionization enhances combustion by shortening ignition delays. The present study adds detailed kinetic information on the ion-molecule reactions involved. This information has been lacking, especially at the higher pressures and temperatures that are relevant to studies of combustion systems.
Figure 1. Typical low-resolution mass spectrum of the O2+ + C10H14 system. The dashed peak at mass 32 corresponds to the undepleted O2+ signal before the addition of n-butylbenzene. The peak at mass 147 corresponds to secondary reaction of benzylium (C7H7+) with C10H14, see eq 2.1.
The present work allows for extrapolations to be made to the relevant conditions. 2. Experimental Technique and Results Our experiments were conducted in the turbulent ion flow tube (TIFT) which has been described in detail before;18,19,29 therefore, the technique is only briefly summarized here. The TIFT is similar to low-pressure flow tubes except that larger flow rates are used to achieve higher pressures and Reynolds numbers. A liquid nitrogen storage vessel supplies the N2 carrier gas, which is preheated in a sidearm. A few experiments were made in a helium buffer using bottled high purity helium scrubbed in liquid-nitrogen-cooled molecular sieve traps. The precursor ions, O2+, are created upstream in an off-axis corona discharge source and are entrained into the N2 or He flow in the sidearm. The bulk flow enters the flow tube where a gas mixture of N2 and vapor of the neutral reagent n-butylbenzene is injected through a moveable, on-axis tube; this promotes efficient charge transfer to produce n-butylbenzene cations. At the end of the flow tube, most of the gas is removed by a large mechanical pump while a small fraction is sampled through a 150 µm orifice in a truncated nosecone. The core of the ensuing supersonic expansion is sampled through a skimmer into a mass spectrometer. The ions are analyzed by a quadrupole mass filter and counted by a discrete dynode electron multiplier. To elevate the temperature, five zones of heating are used, and the thermocouple that monitors the gas temperature is maintained to (2 K. The main flow tube is heated in three zones: one short zone at the upstream end near the bellows, a long middle section, and a zone inside the vacuum chamber just upstream of the nosecone. The connection between the corona discharge tube and the sidearm is also heated. Finally, it was found that preheating of the buffer gas is needed since the residence time is too small to cope with the decrease in heat transfer which in turn is due to high pressures. The preheater consists of two Mellen split type (clam shell) tubular heating elements that surround a tubular piece of copper; the gas flows through narrow channels (which traverse the copper tube along the axis) that have a radial-spoke cross-section.29 A typical mass spectrum is shown in Figure 1, with and without the butylbenzene reactant gas. In the absence of butylbenzene, the O2+ signal is dominant (>98%). Common impurities are H3O+(H2O)0,1 and O2+(H2O). The ion at 60 amu
Two-Channel Dissociation of C10H14+
J. Phys. Chem. A, Vol. 110, No. 27, 2006 8469
is O2+(N2). Since the relative concentrations of the impurities were usually less than 2% (sometimes much less), no corrections to the recorded branching ratios were made. When butylbenzene is added, product ions at 43, 78, 91, 92, 105, 119, 134, and 147 amu are observed. The dissociative and nondissociative chargetransfer products at 91/92 and 134 amu, respectively, dominate. In Figure 1, the 91 and 92 amu peaks are merged. This resolution reduces mass discrimination and is used to measure the overall S/D. Higher resolution spectra are used to separate the two peaks, and an isotope correction is made. The mass 43, 78, 105, and 119 amu peaks are present at the same levels as impurities, ca. 0.5-2% at low temperatures. At higher temperatures, the yields of m/z ) 78, 105, and 119 increase and can be investigated; these originate from the breaking of the various C-C bonds in the side chain; in these cases, the aromatic fragments mainly contain the charge since these are more stable than the alkyl species. The m/z ) 43 peak of the propyl ion (C3H7+), which in Figure 1 is barely detectable (∼0.1% of total signal), indicates that as the benzylic C-C bond breaks, see reaction 1.1, less than 1% of the time the charge remains on the alkyl fragment; this conforms with Stevenson’s rule: the fragmentation of an ion into two or more channels will favor the formation of the neutral with the highest ionization energy. There is another peak between 55 and 60 amu that could be due to the presence of C4H9+ (m/z ) 57) but here the resolution is too low to differentiate between the butyl ion and impurities. The peak at mass 147 is likely31 due to a reaction between benzylium and neutral butylbenzene
C7H7+(Bz+) + C10H14 f C11H15+ + C6H6
(2.1)
Branching ratios of the ion products were recorded as a function of the neutral reagent concentration. Secondary chemistry was taken into account by extrapolating to zero concentration. The accessible temperature and pressure ranges were limited by the allowable intensity of impurity ions ( 2000 K. In a combustion situation, both processes may occur. It appears worth noting that the positive temperature coefficient of the preexponential factor of Kc and the negative temperature coefficient of frigid lead to a comparably small preexponential factor and apparent activation energy of kdiss,∞(91) (for which E0(91)/k would be equal to 20 660 K). 4.2. Branching Ratios 91/92. Equation 3.10 may serve as our molecular thermometer for an estimate of the relative contributions of the charge-transfer components 2.2a and 2.2b, such as described in section 3.3. In the following, we illustrate the sensitivity of the ratio 91/92 on the contributions from resonant (reaction 2a, branching ratio ga) and complex-forming charge transfer (reaction 2b, branching ratio gb). Leaving gc unchanged at 0.13 and considering the temperature T ) 448 K,
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Fernandez et al.
Figure 7. Effective branching ratios 91/92 for chemical activation experiments as a function of temperature. Lower curve ) modeling results for ga ) 0, gb ) 1, and gc ) 0, i.e., completely complex-forming charge transfer; middle curve ) modeling results for ga ) 0.4, gb ) 0.47, and gc ) 0.13; upper curve ) modeling results for ga ) 1, gb ) 0, and gc ) 0, i.e., completely resonant charge transfer.
one has average energies of 3.736 eV at ga ) 0.6 and 3.586 eV at ga ) 0.4. Using these energies for Eac in eq 3.10, one would have 91/92 ) 0.58 in the former and 91/92 ) 0.46 in the latter case. The case ga ) 1, corresponding to exclusively resonant charge transfer, would lead to an average energy of 3.872 eV and 91/92 ) 0.71. In reality, the energy dependent branching ratio 91/92 from eq 3.10 needs to be averaged over the energy distribution generated by charge transfer. Doing this, for T ) 448 K (and leaving gc ≈ 0.13 unchanged), we obtain 91/92 ) 0.63 and 0.54 for ga ) 0.6 and 0.4, respectively. As the experimental value of 0.55 is close to the latter case, we employ ga ) 0.4, gb ) 0.47, and gc ) 0.13 for our modeling of the S/D curves. The assumption of completely resonant charge transfer (ga ) 1) with an average 91/92 ) 0.72 apparently is ruled out by our measurements. This is also confirmed by our measurements of S/D discussed below. Figure 7 shows the effective branching ratios of our experiments as a function of temperature, comparing modeling results for (ga, gb, gc) ) (0.4, 0.47, 0.13) with results for ga ) 1, i.e., completely resonant charge transfer, and gb ) 1, i.e., completely complex-forming charge transfer. Neither ga ) 1 nor gb ) 1 are compatible with the measured 91/92 ) 0.55 at 448 K given above and (91/91)0 ) 0.75 at 548 K such as extrapolated to time zero in Figure 4. 4.3. Stabilization vs Dissociation. Our modeling of the experimental S/D curves as a function of buffer gas, pressure, and temperature follows the procedure described in ref 22 and in section 3.3. The averaging over the distribution g(E,T) from the charge-transfer components 2.2a-2.2c is done with the branching ratios ga ) 0.4, gb ) 0.47, and gc ) 0.13, such as suggested in section 4.2, and the averaging over the energy distributions described in section 3.2. S/D then is given by22
S/D ) Z[M]
∫0∞ dE g(E,T)γc(E)/[k91(E) + k92(E)]
(4.8)
with γc(E) from eq 3.5 using E0 ) E0(92) and s* ≈ 8.0, and k91(E) + k92(E) from eqs 3.1 and 3.2. The results are shown in Figure 8 where the experimental points from Figure 2 are compared with the modeling results from eq 4.8. The modeling in Figure 8 has been done employing the average energy transferred per collision -〈∆E〉/hc ) 285 cm-1 for M ) N2. This is value found for the C8H10+ system in ref 22. Performing analogous modeling for the limited experimental
Figure 8. Stabilization (S) vs dissociation (D) yields in chemical activation experiments. Data from Figure 2 modeled with ga ) 0.4, gb ) 0.47, gc ) 0.13, and -〈∆E〉/hc ) 285 cm-1, see text.
data for M ) He given in Table 1 yields a similar result, -〈∆E〉/ hc ) 180 cm-1, to that found for C8H10+ in ref 22. One notes that the experimental S/D curves and their temperature dependence can be reproduced within the experimental scatter. One should note that we have evaluated the curve at the highest temperature (548 K), by fixing kpyr at 210 s-1 such as given by eq 4.7. At this temperature, the thermal dissociation becomes too fast to allow for a separate determination of kpyr and (S/ D)0. The agreement of the modeled and measured S/D curves in Figure 8 is by no means perfect. First, there is considerable experimental scatter. Second, we have assumed that the chargetransfer branching ratios ga, gb, and gc are temperature independent. Small temperature dependences of ga would improve the agreement. We have not employed such corrections since we have too little conclusive evidence for this behavior and gc remains uncertain. Nevertheless, our results support the conclusion that collisional energy transfer of vibrationally highly excited molecular ions is not very much more efficient with respect to 〈∆E〉 than the corresponding transfer in neutrals. However, somewhat larger values of |〈∆E〉| seem to be observed. On the other hand, the collision frequencies Z for ions are much larger (given by the Langevin rate constant in the present case) than for neutrals (mostly given by Lennard-Jones collision numbers), resulting in an overall rate that is larger than for neutral systems. The present modeling also allows for a prediction of S/D over larger pressure ranges such as this has been demonstrated for the C8H10+ system in ref 22. Figure 9 shows a plot of S/D over much wider pressure ranges than studied here. One may also employ the S/D curves to investigate the relevance of the three components of the charge-transfer processes 2.2a-2.2c as has been done above using the branching ratio of 91/92. Figure 10 demonstrates that purely resonant charge transfer (ga ) 1) is unable to reproduce the data, particularly at low pressures, even if very large values of |〈∆E〉| corresponding to γc ) 1 are employed. Likewise, purely complex-forming charge transfer is unable to account for the observed S/D and 91/92. The combination of both S/D and 91/ 92 measurements in the present work, therefore, supports the conclusion from ref 22 that charge transfer between O2+ and alkylbenzenes is characterized by several components such as symbolized by reactions 2.2a, 2.2b, and 2.2c. Channels 2.2a and 2.2b apparently contribute in about equal amounts.
Two-Channel Dissociation of C10H14+
J. Phys. Chem. A, Vol. 110, No. 27, 2006 8475 2303EP4 and Grant Award FA8655-03-1-3034. Financial support by the Deutsche Forschungsgemeinschaft (SFB 357 “Molekulare Mechanismen unimolekularer Reaktionen”) as well as help by A. I. Maergoiz are also gratefully acknowledged. 6. Appendix: Molecular Parameters
Figure 10. As in Figures 2 and 8 with a modeling assuming completely resonant charge transfer (ga ) 1, see text) and strong collisions (-〈∆E〉/ hc ) 5000 cm-1).
1. Frequencies (in cm-1): n-C10H14: 3144, 3131, 3123, 3109, 3108, 3054, 3047, 3027, 3003, 3001, 2984, 2979, 2968, 2967, 1633, 1611, 1516, 1509, 1502, 1500, 1489, 1481, 1472, 1413, 1373, 1368, 1344, 1335, 1320, 1297, 1269, 1210, 1204, 1189, 1168, 1116, 1103, 1068, 1056, 1038, 998, 973, 961, 945, 933, 907, 867, 843, 814, 782, 748, 733, 702, 624, 587, 500, 411, 408, 333, 286, 270, 207, 120, 92, 45, 24 (B3LYP/6-31G* calculations from this work with scaling factor 0.9804). n-C10H14+: 3177, 3173, 3162, 3156, 3155, 3082, 3072, 3061, 3058, 3031, 3022, 3010, 2995, 2993, 1639, 1517, 1505, 1497, 1487, 1484, 1476, 1459, 1397, 1395, 1382, 1336, 1328, 1285, 1280, 1252, 1236, 1226, 1202, 1196, 1160, 1092, 1053, 1051, 1004, 995, 986, 986, 982, 976, 948, 879, 847, 805, 789, 777, 767, 732, 627, 541, 527, 435, 364, 361, 343, 244, 234, 179, 119, 69, 64, 40 (B2LYP/6-31G* calculations from ref 15 with scaling factor 0.9804). Transition state for C10H14+ f C7H8+ + C3H6: 3395, 3382, 3359, 3347, 3328, 3301, 3293, 3284, 3264, 3196, 3151, 3129, 3076, 1710, 1663, 1614, 1601, 1573, 1562, 1548, 1509, 1504, 1481, 1471, 1465, 1411, 1362, 1351, 1267, 1253, 1252, 1243, 1124, 1110, 1086, 1064, 1059, 1047, 1040, 1030, 1006, 986, 970, 960, 956, 895, 853, 810, 756, 746, 619, 549, 520, 477, 442, 377, 310, 257, 178, 157, 125, 81, 67, 39 (B3LYP/6-31G* calculations from ref 15 with empirical scaling factor of 1.039 chosen to match k(E) measurements for reaction 1.2). 2. Rotational constants (in cm-1): n-C10H14+: Ae ) 0.116, Be ) 0.019; C7H7+: Ae ) 0.178, Be ) 0.075; n-C3H7: Ae ) 1.044, Be ) 0.278; TS:92 Ae ) 0.089, Be ) 0.021 from ref 15. 3. Energy parameters: IE(O2) ) 12.07 eV, IE(n-C10H14) ) 8.69 eV from ref 38 leading to Ech/hc ) 27260 cm-1. E91 0 ) 1.78 ((0.05) eV from ref 17, E92 0 ) 1.15 ((0.1) eV from ref 15, 1.14 ((0.02) eV from this work.
5. Conclusions
References and Notes
Our measurements of the combined chemical and thermal activation kinetics of vibrationally highly excited n-butylbenzene cations, reacting to form two competing channels, have been analyzed in detail. The branching ratio 91/92 served as a “molecular thermometer” such as demonstrated in earlier studies of this system. In the present case, it provided information on the relative contributions from resonant and complex-forming charge transfer between O2+ and n-butylbenzene. S/D curves in the chemical activation experiments could be reproduced within the experimental scatter from information on specific rate constants k(E) for the dissociation of C10H14+* and on collisional energy transfer. Completely resonant charge transfer or charge transfer through a complex between O2+ and n-C10H14 is not compatible with either the 91/92 branching or the S/D curves. The thermal dissociation experiments provide a high precision value for the energy barrier of the reaction leading to the fragments C7H8+ + C3H6 which is consistent with k(E) measurements of this channel. Our work demonstrates again that the n-butylbenzene cation is a particularly suitable system for studying two-channel competition in the dissociation of molecular cations.
(1) Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics. Theory and Experiments; Oxford University Press: Oxford, 1996. (2) Baer, T.; Dutuit, O.; Mestdagh, H.; Rolando, C. J. Phys. Chem. 1988, 92, 5674. (3) Oh, S. T.; Choe, J. C.; Kim, M. S. J. Phys. Chem. 1996, 100, 13367. (4) Mukhtar, E. S.; Griffith, I. W.; Harris, F. M.; Beynon, J. H. Int. J. Mass Spectrom. Ion Phys. 1981, 37, 159. (5) Griffith, I. W.; Mukhtar, E. S.; March, R. E.; Harris, F. M.; Beynon, J. H. Int. J. Mass Spectrom. Ion Phys. 1981, 39, 125. (6) Griffith, I. W.; Mukhtar, E. S.; Harris, F. M.; Beynon, J. H. Int. J. Mass Spectrom. Ion Phys. 1982, 43, 283. (7) McLuckey, S. A.; Sallans, L.; Cody, R. G.; Burnier, R. C.; Verma, S.; Freiser, B. S.; Cooks, R. G. Int. J. Mass Spectrom. Ion Phys. 1982, 44, 215. (8) McLuckey, S. A.; Ouwerkerk, C. E. D.; Boerboom, A. J. H.; Kistemaker, P. Int. J. Mass Spectrom. Ion Processes 1984, 59, 85. (9) Harrison, A. G.; Lin, M. S. Int. J. Mass Spectrom. Ion Phys. 1983, 51, 353. (10) Chen, J. H.; Hays, J. D.; Dunbar, R. C. J. Phys. Chem. 1984, 88, 4759. (11) Welch, M. J.; Pereles, D. J.; White, E. Org. Mass Spectrom. 1985, 20, 425. (12) Nacson, S.; Harrison, A. G. Int. J. Mass Spectrom. Ion Processes 1985, 63, 85. (13) Uechi, G. T.; Dunbar, R. C. J. Chem. Phys. 1992, 96, 8897. (14) Yoon, O. K.; Hwang, W. G.; Choe, J. C.; Kim, M. S. Rapid Commun. Mass Spectrom. 1999, 13, 1515. (15) Muntean, F.; Armentrout, P. B. J. Phys. Chem. A 2003, 107, 7413. (16) Fridgen, T. D.; McMahon, T. B.; Troe, J.; Viggiano, A. A.; Midey, A. J.; Williams, S. J. Phys. Chem. A 2004, 108, 5600.
Figure 9. Modeled S/D over wide pressure ranges (T ) 448 K, M ) N2, modeling details as in Figure 8).
Acknowledgment. This project was funded by the United States Air Force Office of Scientific Research under Project
8476 J. Phys. Chem. A, Vol. 110, No. 27, 2006 (17) Troe, J.; Ushakov, V. G.; Viggiano, A. A. J. Phys. Chem. A 2006, 110, 1491. (18) Viggiano, A. A.; Miller, T. M.; Williams, S.; Arnold, S. T.; Seeley, J. V.; Friedman, J. F. J. Phys. Chem. A 2002, 106, 11917. (19) Arnold, S. T.; Seeley, J. V.; Williamson, J. S.; Mundis, P. L.; Viggiano, A. A. J. Phys. Chem. A 2000, 104, 5511. (20) Arnold, S. T.; Viggiano, A. A. J. Phys. Chem. A 2001, 105, 3527. (21) Midey, A. J.; Williams, S.; Arnold, S. T.; Viggiano, A. A. J. Phys. Chem. A 2002, 106, 11726. (22) Troe, J.; Viggiano, A. A.; Williams, S. J. J. Phys. Chem. A 2004, 108, 1574. (23) Fernandez, A. I.; Viggiano, A. A.; Miller, T. M.; Williams, S.; Dotan, I.; Seeley, J. V.; Troe, J. J. Phys. Chem. A 2004, 108, 9652. (24) Miasek, P. G.; Harrison, A. G. J. Am. Chem. Soc. 1975, 97, 714. (25) Ahmed, M. S.; Dunbar, R. C. J. Am. Chem. Soc. 1987, 109, 3215. (26) Barfknecht, A. T.; Brauman, J. I. J. Chem. Phys. 1986, 84, 3870. (27) Boering, K. A.; Brauman, J. I. J. Chem. Phys. 1992, 97, 5439. (28) Fernandez, A. I.; Viggiano, A. A.; Maergoiz, A. I.; Troe, J.; Ushakov, V. G. Int. J. Mass Spectrom. 2005, 241, 305.
Fernandez et al. (29) Viggiano, A. A.; Fernandez, A. I.; Troe, J. Phys. Chem. Chem. Phys. 2005, 7, 1533. (30) Arnold, S. T.; Williams, S.; Dotan, I.; Midey, A. J.; Morris, R. A.; Viggiano, A. A. J. Phys. Chem. A 1999, 103, 8421. (31) Arnold, S. T.; Dotan, I.; Williams, S.; Viggiano, A. A.; Morris, R. A. J. Phys. Chem. A 2000, 104, 928. (32) Hueter, U. Creating an airline to the stars. Aerospace Am. 1999, 37, 40. (33) Troe, J. J. Phys. Chem. 1983, 87, 1800. (34) Snider, N. J. Phys. Chem. 1985, 89, 1257. (35) Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1964. (36) Miller, Th. M. In Handbook of Chemistry and Physics; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 2003; Section 10, p 163. (37) Troe, J.; Ushakov, V. G. J. Phys. Chem. A submitted. (38) NIST Chemistry Webbook, Linstrom, P. J.; Mallard, W. G., Eds.; NIST Standard Reference Data Base No 69; NIST: Gaithersburg, MD, 2005; http://webbook.nist.gov.
